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arXiv:cond-mat/0302377 · Physics Letters A

SU(4) coherent effects to the canted antiferromagnetic phase in bilayer quantum Hall systems at ν=2

Kazuki Hasebe

Published Nov 15, 2003• 0 citations
arXivHTMLPDF
DOI
10.1016/j.physleta.2003.10.066

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We develop an effective spin theory to describe magnetic properties of the $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2$ quantum Hall bilayer systems. In the absence of disorder this theory agrees with the microscopic Hartree-Fock calculations, and for finite disorder it predicts the existence of a novel spin Bose-glass phase. The Bose glass is characterized by the presence of domains of canted antiferromagnetic phase with zero average antiferromagnetic order and short range correlations. It has infinite antiferromagnetic transverse susceptibility and finite longitudinal spin susceptibility. Transition from the canted antiferromagnetic phase to the spin Bose-glass phase is characterized by a universal value of the spin conductance.
We present an exact diagonalization study of bilayer quantum Hall systems at filling factor nu = 2 in the spherical geometry. We find the high-Zeeman-coupling phase boundary of the broken symmetry canted antiferromagnet is given exactly by previous Hartree-Fock mean-field theories, but that the state's stability at weak Zeeman coupling has been qualitatively overestimated. In the absence of interlayer tunneling, degeneracies occur between total spin multiplets due to the Hamiltonian's invariance under independent spin rotations in top and bottom two-dimensional electron layers.
Abstract We propose localization measures in phase space of the ground state of bilayer quantum Hall systems at fractional filling factors , to characterize the three quantum phases (shortly denoted by spin, canted and ppin) for arbitrary -isospin λ . We use a coherent state (Bargmann) representation of quantum states, as holomorphic functions in the 8-dimensional Grassmannian phase-space (a higher-dimensional generalization of the Haldane’s 2-dimensional sphere ). We quantify the localization (inverse volume) of the ground state wave function in phase-space throughout the phase diagram (i.e. as a function of Zeeman, tunneling, layer distance, etc, control parameters) with the Husimi function second moment, a kind of inverse participation ratio that behaves as an order parameter. Then we visualize the different ground state structure in phase space of the three quantum phases, the canted phase displaying a much higher delocalization (a Schrödinger cat structure) than the spin and ppin phases, where the ground state is highly coherent. We find a good agreement between analytic (variational) and numeric diagonalization results.